Question

calculate the value of the fraction: \\(\dfrac{1}{\dfrac{1}{30} + \dfrac{1}{42}}\\)

Explanation:

Step1: Find a common denominator for the fractions in the denominator.

The denominators are 30 and 42. The least common multiple of 30 and 42 is 210. So we rewrite the fractions:
$\frac{1}{30} = \frac{7}{210}$ and $\frac{1}{42} = \frac{5}{210}$.

Step2: Add the fractions in the denominator.

$\frac{7}{210} + \frac{5}{210} = \frac{7 + 5}{210} = \frac{12}{210}$. Simplify this fraction: $\frac{12}{210} = \frac{2}{35}$.

Step3: Now we have a complex fraction $\frac{1}{\frac{2}{35}}$.

To divide by a fraction, we multiply by its reciprocal. So $\frac{1}{\frac{2}{35}} = 1\times\frac{35}{2} = \frac{35}{2}$.

Answer:

$\frac{35}{2}$